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Relational Methods in Computer Science

  • Chris Brink
  • Wolfram Kahl
  • Gunther Schmidt

Part of the Advances in Computing Sciences book series (ACS)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Peter Jipsen, Chris Brink, Gunther Schmidt
    Pages 1-21
  3. Roger D. Maddux
    Pages 22-38
  4. Gunther Schmidt, Claudia Hattensperger, Michael Winter
    Pages 39-53
  5. Armando Haeberer, Marcelo Frias, Gabriel Baum, Paulo Veloso
    Pages 54-69
  6. Holger Schlingloff, Wolfgang Heinle
    Pages 70-89
  7. Jules Desharnais, Bernard Hodgson, John Mullins
    Pages 106-114
  8. Rudolf Berghammer, Burghard von Karger
    Pages 115-130
  9. Rudolf Berghammer, Burghard von Karger
    Pages 131-149
  10. Henk Doornbos, Netty van Gasteren, Roland Backhouse
    Pages 150-165
  11. Jules Desharnais, Ali Mili, Thanh Tung Nguyen
    Pages 166-183
  12. Ryszard Janicki, David Lorge Parnas, Jeffery Zucker
    Pages 184-196
  13. Ali Jaoua, Nadir Belkhiter, Habib Ounalli, Théodore Moukam
    Pages 197-210
  14. Patrick Blackburn, Maarten de Rijke, Yde Venema
    Pages 211-225
  15. Michael Böttner
    Pages 226-246
  16. Back Matter
    Pages 247-275

About this book

Introduction

The calculus of relations has been an important component of the development of logic and algebra since the middle of the nineteenth century, when Augustus De Morgan observed that since a horse is an animal we should be able to infer that the head of a horse is the head of an animal. For this, Aristotelian syllogistic does not suffice: We require relational reasoning. George Boole, in his Mathematical Analysis of Logic of 1847, initiated the treatment of logic as part of mathematics, specifically as part of algebra. Quite the opposite conviction was put forward early this century by Bertrand Russell and Alfred North Whitehead in their Principia Mathematica (1910 - 1913): that mathematics was essentially grounded in logic. Logic thus developed in two streams. On the one hand algebraic logic, in which the calculus of relations played a particularly prominent part, was taken up from Boole by Charles Sanders Peirce, who wished to do for the "calculus of relatives" what Boole had done for the calculus of sets. Peirce's work was in turn taken up by Schroder in his Algebra und Logik der Relative of 1895 (the third part of a massive work on the algebra of logic). Schroder's work, however, lay dormant for more than 40 years, until revived by Alfred Tarski in his seminal paper "On the calculus of binary relations" of 1941 (actually his presidential address to the Association for Symbolic Logic).

Keywords

algebra algorithm algorithms calculus computer computer science database databases development language logic relational database semantics software

Editors and affiliations

  • Chris Brink
    • 1
  • Wolfram Kahl
    • 2
  • Gunther Schmidt
    • 2
  1. 1.Department of Mathematics and Applied MathematicsUniversity of Cape TownCape TownSouth Africa
  2. 2.Fakultät für Informatik, Universität der Bundeswehr MünchenNeubibergFederal Republic of Germany

Bibliographic information